Holographic superconductor/insulator transition at zero temperature

Abstract:We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition. The model involves a complex scalar field coupled to a gauge and gravity field in the bulk. In earlier work (arXiv:1211.7076) the scalar field had a strong self-coupling, in which case the backreaction on both the metric and the gauge field can be ignored. In this approximation, it was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We show that this mechanism for emergence of scaling behavior continues to hold without any selfcoupling in the presence of backreaction of gauge field and gravity. Even though there are no zero modes for the metric and the gauge field, the scalar dynamics induces adiabaticity breakdown leading to scaling. This yields scaling behavior for the time dependence of the charge density and energy momentum tensor.

Section: The Equilibrium Critical Point and Its Exponentsmentioning

confidence: 58%

Section: Jhep01(2015)084mentioning

confidence: 99%

Section: Jhep01(2015)084mentioning

confidence: 99%

Section: Jhep01(2015)084mentioning

confidence: 99%

Section: Jhep01(2015)084mentioning

confidence: 99%

See 3 more Smart Citations

Kibble-Zurek scaling in holographic quantum quench: backreaction

Das

Morita

2015

The particle number in Galilean holography

Balasubramanian

McGreevy

2011

Recently, gravity duals for certain Galilean-invariant conformal field theories have been constructed. In this paper, we point out that the spectrum of the particle number operator in the examples found so far is not a necessary consequence of the existence of a gravity dual.We record some progress towards more realistic spectra. In particular, we construct bulk systems with asymptotic Schrödinger symmetry and only one extra dimension. In examples, we find solutions which describe these Schrödinger-symmetric systems at finite density. A lift to M-theory is used to resolve a curvature singularity. As a happy byproduct of this analysis, we realize a state which could be called a holographic Mott insulator.

Geons and spin-2 condensates in the AdS soliton

Hartnett¹,

Horowitz²

2013

We construct geons starting with gravitational perturbations of the AdS soliton. Previous studies of a charged scalar field in the soliton background showed a holographic insulator/superconductor transition at a critical chemical potential. We explore the possibility that dimensional reduction of the geon could model a transition to a d-wave superconductor. We find that although one does get a charged spin-2 condensate, it has higher free energy than the state without the condensate, so there is no phase transition.A geon is a classical solution to the vacuum Einstein equations representing a localized and nondispersing lump of gravitational energy held together by its own gravitational attraction. Geons were originally conjectured to exist by Wheeler, and the first serious attempt to construct them was made by Brill and Hartle [1]. Their geon, however, has only a finite lifetime; at late times the gravitational waves comprising the geon will break free and disperse. This is a common feature of asymptotically flat geons [2]. The tendency of geons to disperse can be remedied with a negative cosmological constant, as anti-de Sitter (AdS) space acts like a confining box. Perturbative geons in global AdS in four dimensions have been recently constructed in [3]. This provides strong evidence that associated with every individual linearized graviton mode in global AdS, there is a one parameter family of exact nonsingular geons 1 .One should be able to construct geons starting with gravitational perturbations of any locally asymptotically AdS ground state. In particular, one can start with the AdS soliton [5,6], which has seen several applications in gauge/gravity duality. It was originally introduced to describe the ground state of a confining gauge theory [5], but in more recent condensed matter applications it has been used to construct the gravitational dual of an insulator/superconductor quantum phase transition [7,8]. In this note we perturbatively construct a class of geons starting with the fivedimensional AdS soliton.Although the geons we find are interesting in their own right, perhaps the most intriguing aspect of these solutions is the potential connection with a d-wave superconductor. The possibility of obtaining a gravitational dual of a d-wave superconductor is exciting because this is what is seen in the high-T c cuprates. While the original holographic superconductor exhibited an s-wave order parameter [9], and later a model with a p-wave order parameter was constructed in [10], the d-wave case remains elusive. The major obstacle to building a d-wave superconductor is that there is no known consistent action for a charged, massive, spin-2 field minimally coupled to gravity. Various authors [11,12] have worked with incomplete actions and found d-wave superconducting condensates, but as of yet no consistent holographic model has been found.An alternative approach towards constructing a d-wave holographic superconductor is to study metric perturbations in Kaluza-Klein theory. Upon dimensional reduction, gr...